As in the previous question, let f, g: [-1, 1] → R be smooth strictly increasing functions, and define a smooth curve y: [-1, 1] → R² by y(t) = (f(t), g(t)). Assume now that y is regular, and let K, be the total signed curvature of gamma. What is the maximum possible value of K,? Select one: O a. 一元 O b. -2 O с. O d. -1 Oе. -/4 O f. -1/2 π/2 Og. 0 Oh. 1/2
As in the previous question, let f, g: [-1, 1] → R be smooth strictly increasing functions, and define a smooth curve y: [-1, 1] → R² by y(t) = (f(t), g(t)). Assume now that y is regular, and let K, be the total signed curvature of gamma. What is the maximum possible value of K,? Select one: O a. 一元 O b. -2 O с. O d. -1 Oе. -/4 O f. -1/2 π/2 Og. 0 Oh. 1/2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![As in the previous question, let ƒ, g: [−1, 1] → R be smooth strictly increasing functions, and define a smooth curve y: [−1, 1] → R² by
y(t) = (f(t), g(t)).
Assume now that y is regular, and let K, be the total signed curvature of gamma. What is the maximum possible value of Ks?
Select one:
Oа. -π
O b. -2
C.
d. -1
-π/2
е. -л/4
- 1/2
O f.
g.
0
O h. 1/2
O i. π/4
O j. 1
Ok. π/2
O I.
2
O m. π
n. K, can take arbitrarily large values, but if y is unit speed then we must have K, ≤ T.
o. K can take arbitrarily large values, even if y is unit speed, so there is no maximum.
p. None of the above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3cb672f7-47ed-4ee3-be4e-71db737c6150%2F7477841a-fe39-403f-abc6-3736a42bae21%2F1uky8jl_processed.png&w=3840&q=75)
Transcribed Image Text:As in the previous question, let ƒ, g: [−1, 1] → R be smooth strictly increasing functions, and define a smooth curve y: [−1, 1] → R² by
y(t) = (f(t), g(t)).
Assume now that y is regular, and let K, be the total signed curvature of gamma. What is the maximum possible value of Ks?
Select one:
Oа. -π
O b. -2
C.
d. -1
-π/2
е. -л/4
- 1/2
O f.
g.
0
O h. 1/2
O i. π/4
O j. 1
Ok. π/2
O I.
2
O m. π
n. K, can take arbitrarily large values, but if y is unit speed then we must have K, ≤ T.
o. K can take arbitrarily large values, even if y is unit speed, so there is no maximum.
p. None of the above.
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